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Math Help - Quadratic Formula and Changing Subject help.

  1. #1
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    Quadratic Formula and Changing Subject help.

    2x^2+3x-3.

    Ive got to -2(sqrt)33/4 but dont know where to go from here.

    And with the equation 2x=b^2-a^3b I need to make x the subject.
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  2. #2
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    Quote Originally Posted by Yppolitia View Post
    2x^2+3x-3.

    Ive got to -2(sqrt)33/4 but dont know where to go from here.

    And with the equation 2x=b^2-a^3b I need to make x the subject.
    I presume you need to solve 2x^2+3x-3 = 0

    There are a couple of ways to do this, but I suspect you are looking for the use of the quadratic formula.

    Given ax^2 + bx + c = 0 then x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    So for 2x^2+3x-3 = 0, a = 2, b = 3, c = -3. Thus:
    x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-3)}}{2 \cdot 2}

    x = \frac{-3 \pm \sqrt{9 + 24}}{4} = \frac{-3 \pm \sqrt{33}}{4}
    For the other problem: 2x=b^2-a^3b
    I don't know what you mean by "make x the subject." I am guessing you mean solve in terms of x?
    2x=b^2-a^3b

    b^2 + (-a^3)b + (-2x) = 0
    This is a quadratic in terms of b. So using the quadratic formula again:
    b = \frac{-(-a^3) \pm \sqrt{(a^3)^2 - 4(1)(-2x)}}{2 \cdot 1}

    b = \frac{a^3 \pm \sqrt{a^6 + 8x}}{2}

    -Dan
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